Question

Q: If you receive on average 2 spam emails per day, what is the probability that you don't receive any spam email on a given day?

Q: Given P(X)=0.2 P(X)=0.2, P(Y)=0.3 P(Y)=0.3 and P(X∩Y)=0.1 P(X∩Y)=0.1, what is P(X|Y)P(X|Y)?

Q: What is the smallest possible sample mean of a bootstrap sample that you can obtain from the sample [1,2,3,4,5]?

Q: An insurance company records on average 10 CTP claims per day. What is the probability that on a particular day at most CTP 10 claims are lodged?

Q: What is the largest possible sample mean of a bootstrap sample that you can obtain from the sample [1,2,3,4,5]?

Q: Compute the expected value of the random variable with the following probability distribution: xx 1 2 3 4 P(X=x)P(X=x) 0.1 0.2 0.2 0.5

Answer #1

1. Suppose the number of junk emails you received per
day has a Poisson distribution with an average of
five per day.
a) What is the probability that you receive 3 junk
emails per day?
b) What is the probability that you receive at least 1
junk email per day?
c) What is the probability that you receive at most 3
junk emails per day?
d) What is the likelihood of receiving between 3 and 6
junk emails per day?

In this question, we
are giving you the task for trying to prevent cybercrime by
performing some data analytics.
You are given the
following sample categorized emails where the emails are
categorized based on if they have the word ‘Free’ or ‘Sale’ in
their headers and if they are actually spam or not (‘Y’ means ‘yes’
the email has the word or is spam, ‘N’ means the email does not
have the word or is not spam):
Email Subject
Word ...

The following chart represents the probability distribution for
the numbers of employees absent per day at a medium-sized
business.
x( # of the employees absent)
f(x) probability
0
0.3
1
0.2
2
0.1
3
0.3
4
0.1
1. What is the probability that at least 4 employees will be
absent?
2. What is the probability that 1 or more employees will be
absent?
3. What is the probability that fewer than 3 employees will be
absent?
4. What is the...

1. In an experiment to study standing waves, you use a string
whose mass per length is µ = (1.8 ± 0.1) × 10−3kg/m. You look at
the fundamental mode, whose frequency f is related to the length L
and tension T of the string by the following equation L = 1 2f s T
µ .
You make a plot with L on the y-axis and √ T on the x-axis, and
find that the best fitting line is...

1. You are performing 5 independent Bernoulli trials with
p = 0.3 and q = 0.7. Calculate the probability of
the stated outcome. Check your answer using technology. (Round your
answer to four decimal places.)
Two successes
P(X = 2) =
2. You are performing 5 independent Bernoulli trials with
p = 0.4 and q = 0.6. Calculate the probability of
the stated outcome. Check your answer using technology. (Round your
answer to four decimal places.)
Three successes
P(X =...

A professional employee in a large corporation receives an
average of µ = 41.7 e-mails per day. An anti-spam protection
program was installed in the company's server and one month later a
random sample of 45 employees showed that they were receiving an
average of ?̅= 36.2 e-mails per day. Assume that ơ = 18.45. Use a
5% level of significance to test whether there has been a change
(either way) in the average number of emails received per day...

A researcher claims that college students walk an average of
7,700 steps per day. You do not believe this claim, and you set out
to conduct a hypothesis test. If the test statistic is equal to 1.9
and you have set up a two-tailed (or
two-sided) alterative hypothesis, what will the
p-value be?

Consider the following probability distribution.
xi
P(X =
xi)
–2
0.2
–1
0.1
0
0.3
1
0.4
The variance is _____.
The expected value is _____.
The foreclosure crisis has been particularly devastating in
housing markets in much of the south and west United States, but
even when analysis is restricted to relatively strong housing
markets the numbers are staggering. For example, in 2017 an average
of three residential properties were auctioned off each weekday in
the city of Boston,...

2. Quantitative Problem: You are given the
following probability distribution for CHC Enterprises:
State of Economy
Probability
Rate of return
Strong
0.25
22%
Normal
0.5
9%
Weak
0.25
-6%
- What is the stock's standard deviation? Round your answer to
two decimal places. Do not round intermediate calculations.
_____%
- What is the stock's coefficient of variation? Round your
answer to two decimal places. Do not round intermediate
calculations.
______
5.
A stock's returns have the following distribution:
Demand for...

2.15 A silver dollar is flipped twice. Calculate the
probability of each of the following occurring:
a) A head on the first flip
b) A tail on the second flip given that the first
toss was a head
c) Two tails
d) A tail on the first and a head on the second
e) A tail on the first and a head on the second or a
head on the first and a tail on the second
f) At least...

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